1. Field of the Invention
The present invention relates to the conversion of signals from digital to analog form and more particularly relates to high-speed wideband data conversion via digital-to-analog converters for and methods of generating analog signals having usable spectra extended beyond the Nyquist frequency.
2. Description of the State of the Art
Conventional digital-analog converters translate digital signals to analog signals by holding, for each converter clock cycle, the values of the digital signals at each converter clock cycle. The corresponding spectrum is represented as being within an envelope in a response of sinc (πf/fck) which has null points at multiples of the clock frequency, e.g., 1 fck, 2 fck, 3 fck, and so on. Due to the uneven response, the usable frequency range is limited from DC, or steady-state, to half of the clock frequency where half the clock frequency, when acting as a sampling frequency, is known as and termed the Nyquist frequency. The usable frequency band is known as and termed the Nyquist bandwidth.
As illustrated in FIG. 1, in a digital signal processing subsystem 10, where a multi-rate digital expander 12, which is an extra digital signal-processing module, can be used to extend the usable frequency range, that is the range that is useful linear signal processing for example. The expander 12 inserts M-1 zero points in the original digital signal 11, x(n), preceding the conventional DAC at a multiple, m, of the original clock rate. The output digital signal 13, xE(m), of the expander is fed to a conventional digital-to-analog converter (DAC) 14 which generates an analog waveform 15, x(t). Due to the higher data rate and relative narrower pulse shape, the prior art approach can extend the usable analog output spectrum by a factor of m as compared to a conventional digital-to-analog converting process. Extra interpolation filters can be added following the expander 12 to further select a specific bandwidth within the extended usable spectrum. However, in order to implement this approach, the digital subsystem 10 requires two different clock rates and the extra expander 12. This expander-DAC subsystem 10 complicates the digital code implementation and introduces a need of a higher clock rate resulting in a higher cost of the entire digital signal processing subsystem 10 and the overall digital signal processing in which it is integrated.
FIG. 2 illustrates an alternative subsystem 20 that shapes in the frequency domain the signal at the analog output 27, X(t), of the DAC 14. FIG. 2 also shows the conventional DAC 14 followed by an analog track-and-reset shaping component 23. The track-and-reset shaping component 23 is used as a means for spectrum envelope shaping. In each clock cycle, the track-and-reset component 23 tracks the analog signal of the DAC 14, i.e., the analog output 27, X(t), in a fraction of a clock period and resets 24 the output 26, Xs(T), to zero 25 for the remainder of the clock period. Typically, the timing ratio of the track cycle and the reset cycle is 1:1. The track-and-reset component 23 follows the conventional digital-to-analog converter 14, performs shaping on the analog output signal 27, X(t), of the digital-to-analog converter 14, and, because of the narrower shape of the analog signal 26, Xs(t), results in a flatter envelope response compared to the conventional digital-to-analog converters. This track-and-reset component can also eliminate the transient distortion if timing is appropriately selected. However, the overall linearity of the processing done by the subsystem 20 can deteriorate due to the inherent non-linearity of the track-and-reset component 23. In particular, it is at high clock rates that the linearity of the processing can be worsened by the limit of dynamic performance of the analog track-and-reset component 23. Furthermore, in the reset cycle, feed-through between the digital-to-analog converter 14 and the output signal 26, Xs(t), can further degrade the overall performance.
With the increased cost of implementing pre-DAC processing such as digital expanders 12 and the performance limitations and degradations of track-and-reset components 23 in post-DAC processing, there remains a need for a digital domain device and method, producing a spectral extension of the usable analog spectrum, to improve digital-to-analog conversion.